# How to write an equation in standard form for a line through (1,-5); slope -3/2?

May 20, 2018

$3 x + 2 y = 7$

#### Explanation:

the easiest way to do this is start with point slope form:

y – y_1 = m(x – x_1)

$\left({x}_{1} , {y}_{1}\right) =$ your point

y – (-5) = -3/2(x – 1)

y +5= -3/2(x – 1)

Now we need to do a little algebra to get the equation in standard form:

$A x + B y = C$, where A, B and C are relatively prime integers.

$y + 5 = - \frac{3}{2} x + \frac{3}{2}$

$\frac{3}{2} x + y = \frac{3}{2} - 5$

now let's multiply through with 2 to get rid if the fractions:

$2 \left(\frac{3}{2} x + y = \frac{3}{2} - 5\right)$

$3 x + 2 y = 3 - 10$

$3 x + 2 y = 7$